Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Tags

CCSS.8.G.B.8

Front

If one side of a right triangle is 6 m and the other side is 8 m, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 m.

Tags

CCSS.8.G.B.7

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.8

Front

In a right triangle, if the lengths of the two legs are 5 m and 12 m, what is the length of the hypotenuse?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13 m.

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

If a right triangle has a hypotenuse of 13 m and one leg of 5 m, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b² = c² - a² = 13² - 5² = 169 - 25 = 144, so b = √144 = 12 m.

Tags

CCSS.8.G.B.7

Front

True or False: You can use the Pythagorean Theorem for any triangle.

Back

False. The Pythagorean Theorem only works for right triangles.

Tags

CCSS.8.G.B.8

Front

What do you do to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

You add the squares of the lengths of the two legs and then take the square root to find the length of the hypotenuse.

Tags

CCSS.8.G.B.8